1 L Jan-22-04 SMD159, 3D Graphics in OpenGL Overview 3D - - PDF document

Jan-22-04 SMD159, 3D Graphics in OpenGL 1 L

INSTITUTIONEN FÖR SYSTEMTEKNIK

3D Graphics in OpenGL

David Carr Fundamentals of Computer Graphics Spring 2004

Based on Slides by E. Angel

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Overview

• 3D applications in OpenGL
• A 3D example, Sierpinski gasket, a fractal
• Introduction to hidden-surface removal

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INSTITUTIONEN FÖR SYSTEMTEKNIK

3D Applications in OpenGL

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Three-Dimensional Applications

• In OpenGL, two-dimensional applications are a special

case of three-dimensional graphics

• Not much changes
• Use glVertex3*( )
• Have to worry about the order in which polygons are drawn or

use hidden-surface removal

• Polygons should be simple, convex, flat

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Sierpinski Gasket (2D)

• Start with a triangle
• Connect bisectors of sides and remove central triangle
• Repeat

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Example

• Five subdivisions

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The Gasket as a Fractal

• Consider:
• The filled area (black)
• The perimeter (the length of all the lines around the filled

triangles)

• As we continue subdividing
• The area goes to zero
• But the perimeter goes to infinity
• This is not an ordinary geometric object
• It is neither two- nor three-dimensional
• It is a fractal (fractional dimension) object

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Gasket Program

import java.awt.*; import java.awt.event.*; import net.java.games.jogl.*; public class Gasket2 { public static void main(String[] args) { Frame gasketFrame = new Frame("Sierpinski Gasket"); GLCanvas drawable = GLDrawableFactory.getFactory(). createGLCanvas(new GLCapabilities()); drawable.addGLEventListener(new GasketRenderer()); gasketFrame.add(drawable); gasketFrame.setSize(500, 500); gasketFrame.show(); }

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Triangle Subdivision (part of GasketRenderer)

private void divide_triangle(double[] a, double[] b, double[] c, int m) { // triangle subdivision using vertex numbers double [] v0 = new double[2], v1 = new double[2], v2 = new double[2]; int j; if(m>0) { for(j=0; j<2; j++) v0[j]=(a[j]+b[j])/2; for(j=0; j<2; j++) v1[j]=(a[j]+c[j])/2; for(j=0; j<2; j++) v2[j]=(b[j]+c[j])/2; divide_triangle(a, v0, v1, m-1); divide_triangle(c, v1, v2, m-1); divide_triangle(b, v2, v0, m-1); } else { // …

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Draw a Triangle (divide_triangle Continued)

else { // draw triangle at end of recursion gl.glBegin(GL.GL_TRIANGLES); gl.glVertex2dv(a); gl.glVertex2dv(b); gl.glVertex2dv(c); gl.glEnd(); } }

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GasketRenderer Class

static class GasketRenderer implements GLEventListener { private GL gl; // interfaces, load in every method! private GLU glu; // initial triangle private static final double[] pt1 = {-1.0, -0.58}, pt2 = {1.0, -0.58}, pt3 = {0.0, 1.15}; private static final int RECURSION_LEVELS = 4; public void displayChanged(…) {} public void reshape(…) {} …

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Display() and init() Methods

public void display(GLDrawable drawable) { gl = drawable.getGL(); glu = drawable.getGLU(); gl.glClear(GL.GL_COLOR_BUFFER_BIT | GL.GL_DEPTH_BUFFER_BIT); divide_triangle(pt1, pt2, pt3, RECURSION_LEVELS); gl.glFlush(); } public void init(GLDrawable drawable) { gl = drawable.getGL(); glu = drawable.getGLU(); gl.glMatrixMode(GL.GL_PROJECTION); gl.glLoadIdentity(); glu.gluOrtho2D(-2.0, 2.0, -2.0, 2.0); gl.glMatrixMode(GL.GL_MODELVIEW); gl.glClearColor (1.0f, 1.0f, 1.0f, 1.0f); gl.glColor3f(0.0f,0.0f,0.0f); }

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Moving to 3D

• We can easily make the program three-dimensional by

using double point3 = new double[3]; glVertex3f glOrtho

• But that would not be very interesting
• Instead, we can start with a tetrahedron

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3D Gasket

• We can subdivide each of the four faces
• Appears as if we remove a solid tetrahedron from the

center leaving four smaller tetrahedtra

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Example

after 5 interations

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Modifications to Declarations & Projection

// initial tetrahedron private static final double[][] tetra = { {0., 0., 0.} , {250., 150., 100.} , {250., 500., 0.} , {500., 0., 0.} }; … public void init(GLDrawable drawable) { gl = drawable.getGL(); glu = drawable.getGLU(); gl.glMatrixMode(GL.GL_PROJECTION); gl.glLoadIdentity(); gl.glOrtho(0.0, 500.0, 0.0, 500.0, -500.0, 500.0); gl.glMatrixMode(GL.GL_MODELVIEW); gl.glClearColor(1.0f, 1.0f, 1.0f, 1.0f); }

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Triangle Code

private void triangle(double[] a,double[] b,double[] c) { gl.glBegin(GL.GL_TRIANGLES); gl.glVertex3dv(a); gl.glVertex3dv(b); gl.glVertex3dv(c); gl.glEnd();

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Subdivision Code

private void divide_triangle(double[] a, double[] b, double[] c, int m) { // triangle subdivision using vertex numbers double [] v0 = new double[3], v1 = new double[3], v2 = new double[3]; int j; if(m>0) { for(j=0; j<3; j++) v0[j]=(a[j]+b[j])/2; for(j=0; j<3; j++) v1[j]=(a[j]+c[j])/2; for(j=0; j<3; j++) v2[j]=(b[j]+c[j])/2; divide_triangle(a, v0, v1, m-1); divide_triangle(c, v1, v2, m-1); divide_triangle(b, v2, v0, m-1); } else { triangle(a, b, c); } // draw tri. @end of recursion }

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Tetrahedron Code

private void tetrahedron(int m) { gl.glColor3f(1.0f, 0.0f, 0.0f); divide_triangle(tetra[0], tetra[1], tetra[2], m); gl.glColor3f(0.0f, 1.0f, 0.0f); divide_triangle(tetra[0], tetra[3], tetra[2], m); gl.glColor3f(0.0f, 0.0f, 1.0f); divide_triangle(tetra[1], tetra[2], tetra[3], m); gl.glColor3f(0.0f, 0.0f, 0.0f); divide_triangle(tetra[0], tetra[1], tetra[3], m); }

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Almost Correct

• Because the triangles are drawn in the order they are defined in

the program, the front triangles are not always rendered in front

• f triangles behind them

get this want this

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INSTITUTIONEN FÖR SYSTEMTEKNIK

Introduction to Hidden-Surface Removal

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Hidden-Surface Removal

• We want to see only those surfaces in front of other surfaces
• OpenGL uses a hidden-surface method called the z-buffer

algorithm that saves depth information as objects are rendered so that only the front objects appear in the image

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Using the z-buffer algorithm

• The algorithm uses an extra buffer, the z-buffer, to store depth information

as geometry travels down the pipeline

• Enabled in GasketRender.init()
• gl.glEnable(GL.GL_DEPTH_TEST)
• Cleared in GasketRender.display()
• glClear(GL.GL_COLOR_BUFFER_BIT |

GL.GL_DEPTH_BUFFER_BIT)

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Questions?